More information on the previous problem I posted. Please help me out, thank you?

Question

Suppose that monthly sales volume for a product is normally distributed, with a mean of 500 units and a standard deviation of 50 units. If x denotes the number of units sold in a month, what are the following probabilities:

P(x < 450)

P(x > 600)
P(400 < x < 450)

each are separate and have a standard deviation of 50 units. thank you

Answer 1

Here is what you are supposed to use to answer this question.

67% of a normal distribution falls between +/- 1 standard deviation.
95% of a normal distribution falls between +/- 1 standard deviation.

I'll do the first one to show you how to use these. 450 is -1 standard deviations from the mean. Since 67% is between -1 and +1 standard deviations, then 33% must be outside this range, half on the bottom and half on the top. So the answer is 1/2 of 33% or 16.5%.

The second one is just the same, but greater than 2 standard deviations. The last is and amount between 0 and 1 standard deviations. Draw a picture and this becomes fairly easy.

Answer 2

z = (x-500)/50 follows standard normal distribution

P(x < 450) = P(z < -1) = 0.1587 (from normal tables)

P(x > 600) = P(z>2) = 0.0228 (from normal tables)

P(400 < x < 450) = P(-2

Answer 3

Convert the values to z-scores and look up the probabilities using the table for the standard normal distribution.

Answer 4

Sit down and do you'r homework!! nobody it's going to do it for you!!

Answer 5

uh... what?